Question

For the function f(x) = (x − 2)2 + 4, identify the vertex, domain, and range.
a. The vertex is (–2, 4), the domain is all real numbers, and the range is y ≥ 4.
b. The vertex is (–2, 4), the domain is all real numbers, and the range is y ≤ 4.
c. The vertex is (2, 4), the domain is all real numbers, and the range is y ≤ 4.
d.The vertex is (2, 4), the domain is all real numbers, and the range is y ≥ 4.

Answer 1

@ali2x2

Answer 2

we can rewrite your parabola as below:
\[\Large y - 4 = {\left( {x - 2} \right)^2}\]

Answer 3

now, if we make this change of variable:
\[\Large \left\{ \begin{gathered}
Y = y - 4 \hfill \\
X = x - 2 \hfill \\
\end{gathered} \right.\]
where X, and Y are the new variables, then your parabola can be rewritten as below:
\[\Large Y = {X^2}\]

Answer 4

the graph of that parabola is: